The coordinates of the intersection of two lines are equal to the solution obtained by solving the simultaneous equations representing the two lines.
Example ①
Find the intersection of y = 2x − 1 and y = −x + 5.
Answer: Simultaneous equations: 2x−1=−x+5 → 3x=6 → x=2, y=3. Intersection (2, 3)
Find the intersection of y = 2x − 1 and y = −x + 5.
Answer: Simultaneous equations: 2x−1=−x+5 → 3x=6 → x=2, y=3. Intersection (2, 3)
Key Points
- Coordinates of the intersection = solution of the simultaneous equations
- Checking an approximate intersection on the graph before calculating helps reduce errors
Practice Problems
- Find the intersection of y = x + 2 and y = −2x + 8.
- Find the intersection of y = 3x − 1 and y = x + 3.
Answers and Explanations
- Answer: (2, 4). x+2=−2x+8→3x=6→x=2,y=4.
- Answer: (2, 5). 3x−1=x+3→2x=4→x=2,y=5.